Phylogenetic analysis is a key tool in multiple areas including disease monitoring and drug design; its goal is to infer evolutionary relationships among multiple species, as well as to provide insights into the mechanisms driving the process of molecular evolution. This proposal is informed by two recent trends in phylogenetic analysis. On one hand, most current approaches for phylogenetic analysis require sequence alignments as input and produce reliable results only for proteins with at least a moderate degree of sequence similarity. On the other hand, the scientific community has started to realize that standard procedures for phylogenetic analysis, which first construct a sequence alignment and then use this single point estimate to guide the construction of the phylogenetic tree, can introduce serious biases and make researchers overconfident about the inferred evolutionary history. Indeed, alignment and tree construction are two interrelated problems that should be tackled jointly rather than sequentially. The proposed work represents the first attempt to include structural protein alignments in phylogenetic analysis while jointly accounting for uncertainty in both alignment and tree construction. Our approach employs Markov chain Monte Carlo algorithms to generate samples from the posterior distribution of alignments and trees given the sequences and structures, providing a straightforward procedure to compute probabilities of hypotheses of interest. Specific aims of this project include: 1) To develop novel methods for using unaligned proteins to improve our understanding of the evolutionary relationship between protein sequence and tertiary structure. 2) To develop models for phylogenetic analysis that incorporate sequence and structure information and account for uncertainty in the alignment in the construction of phylogenetic trees and the estimation of evolutionary parameters. 3) To develop new computational algorithms for analyzing a large number of unaligned proteins. 4] To train interdisciplinary scientists capable of using sophisticated statistical methods to solve complex problems in evolutionary biology.